Earlier this week, France manager Didier Deschamps named Mbappe as Hugo Lloris' replacement, with Griezmann serving as his assistant.
Griezmann has been with the France team since 2014 and has won 117 caps, scoring 42 goals.
Mbappe has played 66 times and scored 36 goals since his debut in 2017.
Both players played key roles as France won the World Cup in 2018 and lost another final last year to Argentina.
"I spoke with Antoine. He was disappointed and it's understandable," Mbappe said at a press conference on Thursday. "I told him that I would have had the same reaction.
"He is perhaps the player who has been the most important in the Deschamps era. But I am not his superior. We will be hand in hand, he and I, to try to make this French team reign at world level.
"If he has something to say in front of the group, I will sit down and listen. We must not close the door to anyone. Everyone is free to express themselves."
Mbappe will assume his new role against Netherlands on Friday when France begin the qualification stage for the 2024 European championships.
